Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
248 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 90 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C3×C5×C22⋊Q8 | C2 | semidirect |
| 2. C2×C3×#688 | C2 | semidirect |
| 4. C22×C3×#168 | C2 | semidirect |
| 5. C3×#3967 | C2 | semidirect |
| 6. C3×#3941 | C2 | semidirect |
| 7. C3×#3940 | C2 | semidirect |
| 8. #65337 | C3 | direct (N × H) |
| 23. C5×C22⋊Q8 | C2×C3 | semidirect |
| 24. C2×#688 | C2×C3 | semidirect |
| 26. C22×#168 | C2×C3 | semidirect |
| 27. #3967 | C2×C3 | semidirect |
| 28. #3941 | C2×C3 | semidirect |
| 29. #3940 | C2×C3 | semidirect |
| 45. C3×#168 | D4 | semidirect |
| 48. C3×C22⋊Q8 | D5 | semidirect |
| 69. C22×C3×C5 | SD16 | semidirect |
| 108. #168 | C3×D4 | semidirect |
| 111. C22⋊Q8 | C3×D5 | semidirect |
| 139. C22×C5 | C3×SD16 | semidirect |
| 163. C3×C5 | #465 | semidirect |
| 169. C22×C3 | #688 | semidirect |
| 203. C5 | C3×#465 | semidirect |
| 209. C22 | C3×#688 | semidirect |
| 217. C3 | #65337 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C5×C22⋊Q8 | 2 |
| C2×C3×#688 | 2 |
| C3×#4076 | 2 |
| C22×C3×#168 | 2 |
| C3×#3967 | 2 |
| C3×#3941 | 2 |
| C3×#3940 | 2 |
| #65337 | 3 |
| C3×#465 | 5 |